Lessons

1. Basics
2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

Cylinders and Cones

Objective:

• Learning and using the parts of cylinders and cones, finding areas and volumes of cylinders and cones

Lesson 12-2 Cylinders and Cones

Cylinder: A prism except that its bases are circles instead of polygons

Right Cylinder: A cylinder that forms a 90º between the base and the side.

Altitude: The segment joining the centers of the circular bases in a right cylinder. The altitude is also the height.

Right Cylinder                            Oblique Cylinder

Cone: A pyramid except that its base is  a circle instead of a polygon.

 Theorem 12-5 The Lateral area of a cylinder equals the circumference of a base times the height of the cylinder.  (L.A.= 2rh)   Theorem 12-6 The Volume of a cylinder equals the area of a base times the height of that cylinder. (V=r2h) The height: 10 The radius: 5 Lateral Area=2rh = 2(5)(10)=100 Volume= r2h =(52)(10)= 250   Theorem 12-7 The Lateral area of a cone equals half the circumference of the base times the slant height.  (L.A.= 1/2(2r)l) or (L.A.=rl)   Theorem 12-8 The Volume of a cone equals one third the area of the base times the height of the cone. (V= 1/3r2h)     The height: 8 The slant height:10 The radius: 5 Lateral Area=r l = (5)(10)=500 Volume= 1/3 r2h =1/3 (52)(8)= 200/3

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